I think it falls under the face covering category, which is still acceptable in most, if not all, instances. Gaiters are very comfortable.
The issue is not one of comfort. What I've heard most often that those types of face coverings are less effective than an N95 for example by 40% or 50%.
Obviously there may be some brands which are better than some face mask brands. I do not know which any given team is wearing of either. If the NFL has set some criteria for what is acceptable and what isn't then that's fine.
EDIT: There seem to be more games in NFL and college that we're seeing some number of live fans in attendance. Many masks and effort to social distance.
It's a little like an on going test to see what works. Generally we're hearing cases going up across the US. While I'm not suggesting this is due to game attendance only, I wonder if it at least part of the reason?
Crowds even outside are still proving facilitate create spread of virus: Sturgis rally and political rallies, protest rallies are not without risks.